Question

can someone please help me find the equation of the perpendicular bisector of a line segment joining the points (-3,0) and (4,0). please included the steps i learn best from examples

Answer 1

what's the mid-point of (-3,0) and (4,0) ?

Answer 2

is it (-1.5,2)?

Answer 3

the x-coordinate is \[{-3+4\over 2}=-1.5\ \checkmark\]

Answer 4

the y-coord will be\[{0+0\over 2}=\color{red}0\]

Answer 5

wait the x-coord is also wrong .... unless you copied the two points wrong for me

Answer 6

Yes i did, i'm such a cluts, I'm sorry its (-3,0) and (0,4)

Answer 7

ok then your midpoint is correct . (-1.5 , 2)

Answer 8

you also need the slope of the line through (-3,0) and (0,4)
...

Answer 9

i got 4/3

Answer 10

right. so what's the slope of a line that's perpendicular to the original segment?

Answer 11

I believe it is a negative reciprocal, so the answer would be -3/4

Answer 12

correct ... so perpendicular bisector has slope -3/4 and passes through mid-point (-1.5,2)

so its equation is.

Answer 13

y=(-3/4)x+0.875...?

Answer 14

\[y-2=-\frac34\left( x+1.5 \right)\]or, if you want to re-write in point-slope form:\[y=-\frac34x+\frac78\]

you are CORRECT ! :)

Answer 15

i'm sorry, but how do you get point-slope form?

Answer 16

and then why would the correct answer on the answer key be 6x-8y-7=0? I don't understand, how one would come to that answer, can you please help?

Answer 17

7/8 is the same as 0.875

Answer 18

to get the answer in the Answer key ... you first get rid of the fractions. by multiplying the equation by 8:\[y=-\frac34x+\frac78 \\ \implies 8y=-6x+7\]

Answer 19

next move all terms to the left:\[6x+8y-7=0\]

Answer 20

oh i see, so to get the final answer i would have to work from the point-slope formula